Problem: 5 people can paint 3 walls in 41 minutes. How many minutes will it take for 8 people to paint 8 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 3\text{ walls}\\ p &= 5\text{ people}\\ t &= 41\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{3}{41 \cdot 5} = \dfrac{3}{205}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 8 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{3}{205} \cdot 8} = \dfrac{8}{\dfrac{24}{205}} = \dfrac{205}{3}\text{ minutes}$ $= 68 \dfrac{1}{3}\text{ minutes}$ Round to the nearest minute: $t = 68\text{ minutes}$